"We've had discussions on counter-terrorism cooperation in a number of venues with the Russians," Psaki told reporters. "We welcome any efforts and willingness and openness to cooperate around the Olympics."
FBI Director James Comey told reporters Thursday the Russians are cooperating with the U.S., echoing a statement made previously to ABC News by a spokesperson for the Russian Embassy in Washington, D.C.
Still, an American official, speaking on condition of anonymity, said there "are clearly sensitivities in our relationship with Moscow," even if Olympics security is of "mutual interest."
"The Volgograd bombings underscore the threat and why it makes sense to work hand-in-hand with Russia to ensure the protection of U.S. citizens participating in and attending the Games in Sochi," the official told ABC News.
U.S. intelligence interpreted October's Volgograd bus bombing, carried out by a female suicide bomber and caught on another Russian drivers' dashboard camera, as Umarov following through on his videotaped threat last July, which ordered his followers to do what they can do stop the Olympics.
That the October explosion and the follow-up attacks in late December took place in Volgograd is especially troubling to Georgetown University scholar Christopher Swift, who has studied the resistance against the Russian government in Chechnya and Dagestan and who also has interviewed scores of militants.
"Anybody traveling by ground to the Olympics likely will have to go through Volgograd," Swift told ABC News.
The bombings in the city, which famously held off the Third Reich's advance during World War II when it was known as Stalingrad, mean that for Umarov's followers the Winter Games "are an operational priority and that they have the capability" to strike outside of their traditional area of activity, Swift said.